AXISYMMETRIC MIRROR STABILIZED BY A SHAPED END WALL

Transcription

1 UCRL-PRES-438 AXISYMMETRIC MIRROR STABILIZED BY A SHAPED END WALL D.D. Ryutov Lawrence Livermore National Laboratory, Livermore, CA 94551, USA (Presented at the ICC Workshop, Madison, WI, May 5-8 4) * Work performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No.W-745-Eng-48.

2 MOTIVATION / SUMMARY Axisymmetric mirrors have a number of advantages (no neoclassical losses; very high magnetic field in the mirror throats; higher critical betas for ballooning modes; engineering simplicity). The particular stabilization scheme* does not require introducing any specific sub-systems and naturally fits into the overall design. It may substantially improve performance of high-beta, Q~ 1 mirrors suitable for burning the radioactive waste. The physics involved may favorably affect the tokamak divertor design, and FRC confinement (plasma stability on the open field lines). This physics can be tested with existing small-scale open-ended systems. *D.D. Ryutov. Axisymmetric MHD stable mirrors. In: Physics of Mirrors, Reversed Field Pinches and Compact Tori (Proc. Intern. Scool of Plasma Physics, Varenna, Italy, Sept. 1-11, 1987),. v., p. 791, Editrici Compositori, Bologna, At that time I have thought that this is just a curiosity.

3 An axisymmetric mirror is usually unstable (the energy principle) Consider a radial displacement of the flux tube ξ ξ r L Z Flux-tube volume: dl V = Sdl = Φ Φ Ur ( ) B The plasma thermal energy is released if the volume V increases for the outward displacement: U/ r > (unstable). We use a paraxial approximation (very accurate). Another version: Pressure-weighted version (Rosenbluth, Longmire): / κdl / B 3 3/ < ( p + p ) κdl/ B < (unstable) (unstable)

4 Contribution of the end wall to the stability integral ξ r Z ξa δl= ξa cot α; δv = Φ cot α ( A =absorber) BA The pdv work is done only in the case if plasma is reflected by the wall (this is why the wall effect may look as a curiosity). However, 98 % of the electrons are reflected by the Debye sheath. This leads to the following modification of the stability integral: ξ A κdl pea cot α ( p + p ) + > 3/ 3/ B B α A The flux-tube length and volume change at α π/! One can expect a stabilizing pdv contribution to emerge. (stable)

5 Is there anything more than a curiosity in all this? κdl pea cot α ( p + p ) + > 3/ 3/ B BA pr 3 LB ~ / (stable) p p ea 3 r BA 5 > / 31 L α ~ ()!! B (No problem with the heat load) Note that direct contact of the plasma with a conducting wall does not mean that the line-tying is present! (Kunkel and Guillory, 1965; Kadomtsev, 1965). For the plasma parameters of interest for fusion research, the sheath voltage effectively decouples the plasma from the conducting wall (Ryutov, 1987). For a complete description of the wall effect, one needs to formulate BC s for the sheath in the tilted field (Farina, Pozzoli, Ryutov, 1993; Cohen, Ryutov, 1995)

6 This stabilization technique can be used in Q~1 mirror facility for the nuclear waste burning The natural plasma loss is sufficient to maintain a required amount of a stabilizing plasma No specific additional systems are needed just a properly shaped plasma absorber

7 Although this study was primarily motivated by mirror physics, it may have an impact on the other fusion systems - Plasma on open field lines in FRCs - Divertors (one of possible ICC contributions to the main-line research) T e y x x=radial, y=poloidal, z=toroidal (z directed away from us) Control surface α n α

8 Dispersion relation (Ryutov, Cohen, 4) inertia Kunkel-Guillory sheath resistivity Effect of the x-point the BRT term Ω + Ω( iω + Ω + iω ) iγ + Γ = Effects associated with radial tilt T e x T e x Mu Ω 1 = ω Ci Lk T, Ω = ω Ci α e kl cot Γ 1 = Λ+ 1 ω Ci u T e kl T Γ, = e Ω, 3 = ω CiG kl, T e cotα ML. Destabilizing is good in the context of reducing the divertor heat load (spreading the heat over a larger area) α< Destabilizing n n α Stabilizing

9 This is an interesting subject for basic research Depending on the shape of the plasma receiver in a linear device, the plasma may be more or less stable Stabilizing Destabilizing LAPD, other devices with open field lines...

10 MOTIVATION / SUMMARY Axisymmetric mirrors have a number of advantages (no neoclassical losses; very high magnetic field in the mirror throats; higher critical betas for ballooning modes; engineering simplicity). The particular stabilization scheme* does not require introducing any specific sub-systems and naturally fits into the overall design. It may substantially improve performance of high-beta, Q~ 1 mirrors suitable for burning the radioactive waste. The physics involved may favorably affect the tokamak divertor design, and FRC confinement (plasma stability on the open field lines). This physics can be tested with existing small-scale open-ended systems. *D.D. Ryutov. Axisymmetric MHD stable mirrors. In: Physics of Mirrors, Reversed Field Pinches and Compact Tori (Proc. Intern. Scool of Plasma Physics, Varenna, Italy, Sept. 1-11, 1987),. v., p. 791, Editrici Compositori, Bologna, At that time I have thought that this is just a curiosity.

11 ABSTRACT We consider a possibility of stabilizing a mirror device by the proper shaping of the end walls. The idea is that the sheath at the wall would reflect the majority of the impinging electrons; then, by the proper shaping of the wall, one can achieve the situation where a flute sliding along the wall in the radially-outward direction, would get shorter and the corresponding PdV work over the electron gas would overweigh the effect of the unfavorable field-line curvature. This general idea was described more than 15 years ago [1] but was thought to be impractical because of a very low electron pressure in the end tank of a mirror device. We have recently revisited this issue and found that, by making the end-wall of a conical shape, with a small opening angle and the apex pointing away from the mirror, one can reach a robust stabilization without compromising the plasma confinement. The axial dependence of the magnetic field near the field maximum should be properly tailored. We consider a possible impact of this improvement on the prospects of a mirror facility for the burning of the nuclear waste of fission reactors and conclude that such a facility may become feasible. [1] D.D. Ryutov. Axisymmetric MHD stable mirrors. In: Physics of Mirrors, Reversed Field Pinches and Compact Tori (Proc. of the Course and Workshop, Intern. School of Plasma Physics, Varenna, Italy, Sept. 1-11, 1987, S. Ortolani and E. Sindoni, Eds.) v., p. 791, Editrici Compositori, Bologna, 1988.

12 Relevant references: D.D. Ryutov. Axisymmetric MHD stable mirrors. In: Physics of Mirrors, Reversed Field Pinches and Compact Tori (Proc. of the Course and Workshop, Intern. School of Plasma Physics, Varenna, Italy, Sept. 1-11, 1987, S. Ortolani and E. Sindoni, Eds.) v., p. 791, Editrici Compositori, Bologna, W. Kunkel, J. Guillory. In: Phenomena in Ionized Gases (Proc. &th Conf. Belgrade, 1965) Vol., p. 7, Belgrade, 1966 B.B. Kadomtsev, ibid, p. 61. H.Berk, D. D. Ryutov, Yu. A.Tsidulko JETP Lett., 5, 3 (199). D.Farina, R.Pozzoli, D. Ryutov. Plasma Phys. Contr. Fusion, 35, 171 (1993). D.Farina, R.Pozzoli, D.D. Ryutov. Phys.Fluids, B5, p.455 (1993). R.H.Cohen, D.D. Ryutov. Phys. Plasmas,, 11 (1995). D.Farina, R.Pozzoli, D. Ryutov. Nuclear Fusion, 33, 1315 (1993). D.D. Ryutov, R.H. Cohen. Contributions to Plasma Physics, 44, 168 (4).